Hatcher-Algebraic-Topology · Problem 2.2.9

Homology

Mathematics — Graph Theory · cellular-homology-computation

Problem

Compute the homology groups of the following 2-complexes: (a) The quotient of

S^2

obtained by identifying north and south poles to a point. (b)

S^1 \times (S^1 \vee S^1)

. (c) The space obtained from

D^2

by first deleting the interiors of two disjoint subdisks in the interior of

D^2

and then identifying all three resulting boundary circles together via homeomorphisms preserving clockwise orientations of these circles. (d) The quotient space of

S^1 \times S^1

obtained by identifying points in the circle

S^1 \times \{x_0\}

that differ by

2\pi/m

rotation and identifying points in the circle

\{x_0\} \times S^1

that differ by

2\pi/n

rotation.

Related theory

Cw Complexes And Cellular Homology

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